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Matematicheskie Zametki, 2004, Volume 75, Issue 2, Pages 236–252
DOI: https://doi.org/10.4213/mzm30 (Mi mzm30) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip

M. Yu. Planida

Bashkir State Pedagogical University
Full-text PDF (1668 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm30
Abstract: In this paper, the method of matching asymptotic expansions is used to construct an asymptotics (in a small parameter) of the eigenvalues and eigenfunctions of the Laplace operator in a domain when the boundary-condition type changes on a narrow flattened strip, provided that on the narrow strip of the boundary a Neumann condition is given and on the remaining part of the boundary a Dirichlet condition is given. The width of the strip is taken as the small parameter.
Received: 25.10.2002
English version:
Mathematical Notes, 2004, Volume 75, Issue 2, Pages 213–228
DOI: https://doi.org/10.1023/B:MATN.0000015037.16768.60
Bibliographic databases:
UDC: 517.956
Language: Russian
Citation: M. Yu. Planida, “Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip”, Mat. Zametki, 75:2 (2004), 236–252; Math. Notes, 75:2 (2004), 213–228
Citation in format AMSBIB
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\transl
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Linking options:
  • https://www.mathnet.ru/eng/mzm30
  • https://doi.org/10.4213/mzm30
  • https://www.mathnet.ru/eng/mzm/v75/i2/p236
    • This publication is cited in the following 3 articles:
    1. E. Bonnetier, Charles Dapogny, Michael S. Vogelius, “Small perturbations in the type of boundary conditions for an elliptic operator”, Journal de Mathématiques Pures et Appliquées, 167 (2022), 101  crossref
    2. R. R. Gadyl'shin, E. A. Shishkina, “On Friedrichs inequalities for a disk”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 44–58  mathnet  crossref  isi  elib
    3. M. Yu. Planida, “Asymptotics of the eigenelements of the Laplacian with singular perturbations of boundary conditions on narrow and thin sets”, Sb. Math., 196:5 (2005), 703–741  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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